Q: Which of the following best describes the end behavior of $$m(x) = x^3$ - 2x$$?

$$m(x) \to \infty as$$ $$x \to \infty$$, $$m(x) \to -\infty as$$ $$x \to -\infty$$

Question 1

Given the function $$f(x) = -2x^2$ + 4x - 3$$, what are the coordinates of the vertex of its graph?

Accepted Answer

$$(1, -1)$$

Question 2

For the function $$f(x) = -2x^2$ + 4x - 3$$, what is the maximum or minimum value, and what is it equal to?

Accepted Answer

Maximum value, $$-1$$

Question 3

A rectangular garden is enclosed by 400 ft of fencing. Let $$w be $$the width and $$l$$ the length. Which quadratic function expresses the area $$A in $$terms of $$w$$?

Accepted Answer

$$A(w) = w(200 - w)$$

Question 4

Given the graph of $$g(x) ($$first image), which of the following best describes the domain and range of its inverse?

Accepted Answer

Domain: $$[0, \infty)$$, Range: $$[0, \infty)$$

Question 5

The daily profit for a manufacturer is given by $$P(x) = -8x^2$ + 8000x - 5000$$, where $$x is $$the number of units produced. How many units should be produced each day to yield a maximum profit?

Accepted Answer

$$x = 500$$

Question 6

Let $$m(x) = x^3$ - 2x. $$Which of the following statements is true about the symmetry of $$m(x)$$?

Accepted Answer

$$m(x) is an $$odd function

Question 7

Which equation represents the function obtained by reflecting $$y = x$$ over the $$x-$$axis, then shifting it 4 units right and 2 units down?

Accepted Answer

$$y = -(x-4) - 2$$

Question 8

Given $$f(x) = \frac{3}{x-9}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 9$$

Question 9

Are $$p(x) = x + 3$$ and $$q(x) = x - 2$$ inverses of each other?

Accepted Answer

No, because $$p(q(x)) 
eq x$$

Question 10

Let $$f(x) = \frac{2x^2$ + 8x - 2}{x-4}. $$What is the domain of $$f(g(x)) if$$ $$g(x) = x^2$ - 4$$?

Accepted Answer

$$x 
eq 2, x 
eq -2$$

Question 11

Evaluate $$\ln 9 - \frac{1}{4} \log_e 2.$$

Accepted Answer

$$2\ln 3 - \frac{1}{4}\ln 2$$

Question 12

For the function $$y = \frac{2x^2$ - 12}{x^2$ - 9}$$, what are the equations of all asymptotes?

Accepted Answer

Vertical: $$x = 3, x = -3$$; Horizontal: $$y = 2$$

Question 13

Which of the following best describes the end behavior of $$m(x) = x^3$ - 2x$$?

Accepted Answer

$$m(x) 	o \infty as$$ $$x 	o \infty$$, $$m(x) 	o -\infty as$$ $$x 	o -\infty$$

Question 14

If $$f(x) = \frac{3}{x-9}$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, -\frac{1}{3})$$

Question 15

Which transformation sequence produces the graph of $$y = -(x-4) - 2$$ from $$y = x$$?

Accepted Answer

Reflect over $$x-$$axis, shift right 4, shift down 2

Question 16

Given the graph in the second image, what is the domain of the function $$h(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 17

Given $$f(x) = -2x^2$ + 4x - 3$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, -3)$$

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